Given $ m \angle AOB = 5x - 36$, $ m \angle BOC = 2x + 51$, and $ m \angle AOC = 120$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {5x - 36} + {2x + 51} = {120}$ Combine like terms: $ 7x + 15 = 120$ Subtract $15$ from both sides: $ 7x = 105$ Divide both sides by $7$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 2({15}) + 51$ Simplify: $ {m\angle BOC = 30 + 51}$ So ${m\angle BOC = 81}$.